Humanoid robots are gaining much interest nowadays. This is partly motivated by the ability of such robots to replace humans in dangerous environments being specifically designed for humans, such as man-made or natural disaster scenarios. However, existing robots are far from reaching human skills regarding the robustness to external perturbations required for such tasks, although torque-controlled and even bio-inspired robots hold new promises for research. A humanoid robot robustly interacting with its environment should be capable of handling highly uncertain ground structures, collisions, and other external perturbations. In this paper, a 3D bio-inspired balance controller is developed using a virtual lower limbs musculoskeletal model. An inverse muscular model that transforms the desired torque patterns into muscular stimulations closes the gap between traditional and bio-inspired controllers. The main contribution consists in developing a neural controller that computes the muscular stimulations driving this musculoskeletal model. This neural controller exploits the inverse model output to progressively learn the appropriate muscular stimulations for rejecting disturbances, without relying on the inverse model anymore. Two concurrent approaches are implemented to perform this autonomous learning: a cerebellar model and a support vector regression algorithm. The developed methods are tested in the Robotran simulation environment with COMAN, a compliant child-sized humanoid robot. Results illustrate that - at the end of the learning phase - the robot manages to reject perturbations by performing a full-body compensation requiring neither to solve an inverse dynamic model nor to get force measurement. Muscular stimulations are directly generated based on the previously learned perturbations.